Effective Quantum Electrodynamics Hamiltonians: A Tutorial Review

A with-pair, no-retardation relativistic many-electron Hamiltonian, that is, effective quantum electrodynamics (eQED) Hamiltonian, can be constructed both algebraically and diagrammatically, in a bottom-up fashion without recourse to QED itself. It describes all virtual pair effects due to the instantaneous Coulomb/Gaunt/Breit interaction and is compatible with all wave function or density functional based correlation methods. As such, it serves as the basis for with-pair relativistic quantum chemistry, which is an extension of the traditional no-pair relativistic quantum chemistry. Regardless of the numerical significance of the (nonradiative) virtual pair effects, such an extension represents a conceptually important step for going beyond the no-pair approximation that has been prevailing in relativistic electronic structure calculations of molecular systems. Due to the short range nature, the effective potential Q describing electron vacuum polarization (EVP) and self-energy (ESE) can be fitted into a model operator, which can be included in variational self-consistent field calculations. The subsequent treatments of electron correlation and properties can then be simplified greatly. That is, the major QED effects, including EVP and ESE as well as the Coulomb/Gaunt/Breit screenings of them, can be obtained with little overhead over standard no-pair calculations. It can hence be envisaged that molecular QED will soon emerge as a new and exciting field for ultrahigh precision calculations of molecular spectroscopies and dynamics. (c) 2014 Wiley Periodicals, Inc.